A frequently-encountered problem in metrology is the measurement of the refractive index of a column of air. Several techniques exist for measuring the index under highly controlled circumstances, such as when the air column is contained in a sample cell and is monitored for temperature, pressure, and physical dimension. See for example, an article entitled "An air refractometer for interference length metrology," by J. Terrien, Metrologia 1(3), 80-83 (1965).
Perhaps the most difficult measurement related to the refractive index of air is the measurement of refractive index fluctuations over a measurement path of unknown or variable length, with uncontrolled temperature and pressure. Such circumstances arise frequently in geophysical and meteorological surveying, for which the atmosphere is obviously uncontrolled and the refractive index is changing dramatically because of variations in air density and composition. The problem is described in an article entitled "Effects of the atmospheric phase fluctuation on long-distance measurement," by H. Matsumoto and K. Tsukahara, Appl. Opt. 23(19), 3388-3394 (1984), and in an article entitled "Optical path length fluctuation in the atmosphere," by G. N. Gibson et al., Appl. Opt. 23(23), 4383-4389 (1984).
Another example situation is high-precision distance measuring interferometry, such as is employed in micro-lithographic fabrication of integrated circuits. See for example an article entitled "Residual errors in laser interferometry from air turbulence and non-linearity," by N. Bobroff, Appl. Opt. 26(13), 2676-2682 (1987), and an article entitled "Recent advances in displacement measuring interferometry," also by N. Bobroff, Measurement Science & Tech. 4(9), 907-926 (1993). As noted in the aforementioned cited references, interferometric displacement measurements in air are subject to environmental uncertainties, particularly to changes in air pressure and temperature; to uncertainties in air composition such as resulting from changes in humidity; and to the effects of turbulence in the air. Such factors alter the wavelength of the light used to measure the displacement. Under normal conditions the refractive index of air is approximately 1.0003 with a variation of the order of 1.times.10.sup.-5 to 1.times.10.sup.-4. In many applications the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to 0.003 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and 3 nm, respectively, for a one meter interferometric displacement measurement.
There are frequent references in the art to heterodyne methods of phase estimation, in which the phase varies with time in a controlled way. For example, in a known form of prior-art heterodyne distance-measuring interferometer, the source emits two orthogonally polarized beams having slightly different optical frequencies (e.g. 2 MHz). The interferometric receiver in this case is typically comprised of a linear polarizer and a photodetector to measure a time-varying interference signal. The signal oscillates at the beat frequency and the phase of the signal corresponds to the relative phase difference. A further representative example of the prior art in heterodyne distance-measuring interferometry is taught in commonly-owned U.S. Pat. No. 4,688,940 issued to G. E. Sommargren and M. Schaham (1987). However, these known forms of interferometric metrology are limited by fluctuations in refractive index, and by themselves are unsuited to the next generation of micro-lithography instruments.
Another known form of interferometer for distance measurement is disclosed in U.S. Pat. No. 4,005,936 entitled "Interferometric Methods And Apparatus For Measuring Distance To A Surface" issued to J. D. Redman and M. R. Wall (1977). The method taught by Redman and Wall consists of employing laser beams of two different wavelengths, each of which is split into two parts. Frequency shifts are introduced into one part of the respective beams. One part of each beam reflects from an object and recombines with the other part on a photodetector. From the interference signal at the detector, a phase at a difference frequency is derived which is a measure of the distance to the surface. The equivalent wavelength of the phase associated with the difference frequency is equal to the product of the two laser wavelengths divided by the difference of the two wavelengths. This two-wavelength technique of Redman and Wall reduces measurement ambiguities, but is at least as sensitive to the deleterious effects of refractive index fluctuations of the air as single-wavelength techniques.
Another example of a two-wavelength interferometer similar to that of Redman and Wall is disclosed in U.S. Pat. No. 4,907,886 entitled "Method And Apparatus For Two-Wavelength Interferometry With Optical Heterodyne Processes And Use For Position Or Range Finding," issued to R. Dandliker and W. Heerburgg (1990). This system is also described in an article entitled "Two-Wavelength Laser Interferometry Using Superheterodyne Detection," by R. Dandliker, R. Thalmann, and D. Prongue, Opt. Let. 13(5), 339-341 (1988), and in an article entitled "High-Accuracy Distance Measurements With Multiple-Wavelength Interferometry," by R. Dandliker, K. Hug, J. Politch, and E. Zimmermann. The system of Dandliker et al., as taught in U.S. Pat. No. 4,907,886, employs laser beams of two wavelengths, each of the beams comprising two polarization components separated in frequency by means of acousto-optic modulation. After passing these beams collinearly through a Michelson interferometer, the polarization components are mixed, resulting in an interference signal, i.e. a heterodyne signal. In that the heterodyne signal has a different frequency for each of the two wavelengths, a so-called superheterodyne signal results therefrom having a frequency equal to the difference in the heterodyne frequencies and a phase associated with an equivalent wavelength equal to the product of the two laser wavelengths divided by the difference of the two wavelengths. According to U.S. Pat. No. 4,907,886 (cited above), the phase of the superheterodyne signal is assumed to be dependent only on the position of a measurement object and the equivalent wavelength. Therefore, this system is also not designed to measure or compensate for the fluctuations in the refractive index of air.
Further examples of the two-wavelength superheterodyne technique developed by Redman and Wall and by Dandliker and Heerburgg (cited above) are found in an article entitled "Two-wavelength double heterodyne interferometry using a matched grating technique," by Z. Sodnik, E. Fischer, T. Ittner, and H. J. Tiziani, Appl. Opt. 30(22), 3139-3144 (1991), and in an article entitled "Diode laser and fiber optics for dual-wavelength heterodyne interferometry," by S. Manhart and R. Maurer, SPIE 1319, 214-216 (1990). However, neither one of these examples addresses the problem of refractive index fluctuations.
It may be concluded from the foregoing that the prior art in heterodyne and superheterodyne interferometry does not provide a high speed method and corresponding means for measuring and compensating the optical path length effects of air in a measuring path, particularly effects due to fluctuations in the refractive index of air. This deficiency in the prior art results in significant measurement uncertainty, thus seriously affecting the precision of systems employing such interferometers as found for example in micro-lithographic fabrication of integrated circuits. Future interferometers will necessarily incorporate an inventive, new method and means for measuring and compensating a fluctuating refractive index in a measurement path comprised of a changing physical length.
One way to detect refractive index fluctuations is to measure changes in pressure and temperature along a measurement path and calculate the effect on the optical path length of the measurement path. Mathematical equations for effecting this calculation are disclosed in an article entitled "The Refractivity Of Air," by F. E. Jones, J. Res. NBS 86(1), 27-32 (1981). An implementation of the technique is described in an article entitled "High-Accuracy Displacement Interferometry In Air," by W. T. Estler, Appl. Opt. 24(6), 808-815 (1985). Unfortunately, this technique provides only approximate values, is cumbersome, and corrects only for slow, global fluctuations in air density.
Another, more direct way to detect the effects of a fluctuating refractive index over a measurement path is by multiple-wavelength distance measurement. The basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air. The optical path length is the integrated product of the refractive index and the physical path traversed by a measurement beam. In that the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to determine the physical path length from the optical path length, particularly the contributions of fluctuations in refractive index, provided that the instrument employs at least two wavelengths. The variation of refractive index with wavelength is known in the art as dispersion, therefore this technique will be referred to hereinafter as the dispersion technique.
The dispersion technique for refractive index measurement has a long history, and predates the introduction of the laser. An article entitled "Long-Path Interferometry Through An Uncontrolled Atmosphere," by K. E. Erickson, JOSA 52(7), 781-787 (1962), describes the basic principles and provides an analysis of the feasibility of the technique for geophysical measurements. Additional theoretical proposals are found in an article entitled "Correction Of Optical Distance Measurements For The Fluctuating Atmospheric Index Of Refraction," by P. L. Bender and J. C. Owens, J. Geo. Res. 70(10), 2461-2462 (1965).
Commercial distance-measuring laser radar based on the dispersion technique for refractive index compensation appeared in the 1970's. An article entitled "Two-Laser Optical Distance-Measuring Instrument That Corrects For The Atmospheric Index Of Refraction," by K. B. Earnshaw and E. N. Hernandez, Appl. Opt. 11(4), 749-754 (1972), discloses an instrument employing microwave-modulated HeNe and HeCd lasers for operation over a 5 to 10 km measurement path. Further details of this instrument are found in an article entitled "Field Tests Of A Two-Laser (4416A and 6328A) Optical Distance-Measuring Instrument Correcting For The Atmospheric Index Of Refraction," by E. N. Hernandez and K. B. Earnshaw, J. Geo. Res. 77(35), 6994-6998 (1972). Further examples of applications of the dispersion technique are discussed in an article entitled "Distance Corrections For Single- And Dual-Color Lasers By Ray Tracing," by E. Berg and J. A. Carter, J. Geo. Res. 85(B11), 6513-6520 (1980), and in an article entitled "A Multi-Wavelength Distance-Measuring Instrument For Geophysical Experiments," by L. E. Slater and G. R. Huggett, J. Geo. Res. 81(35), 6299-6306 (1976).
Although instrumentation for geophysical measurements typically employs intensity-modulation laser radar, it is understood in the art that optical interference phase detection is more advantageous for shorter distances. In U.S. Pat. No. 3,647,302 issued in 1972 to R. B. Zipin and J. T. Zalusky, entitled "Apparatus For And Method Of Obtaining Precision Dimensional Measurements," there is disclosed an interferometric displacement-measuring system employing multiple wavelengths to compensate for variations in ambient conditions such as temperature, pressure, and humidity. The instrument is specifically designed for operation with a movable object, that is, with a variable physical path length. However, the phase-detection means of Zipin and Zalusky is insufficiently accurate for high-precision measurement.
A more modern and detailed example is the system described in an article by Y. Zhu, H. Matsumoto, T. O'ishi, SPIE 1319, Optics in Complex Systems, 538-539 (1990), entitled "Long-Arm Two-Color Interferometer For Measuring The Change Of Air Refractive Index." The system of Zhu et al. employs a 1064 nm wavelength YAG laser and an 632 nm HeNe laser together with quadrature phase detection. Substantially the same instrument is described in Japanese in an earlier article by Zhu et al. entitled "Measurement Of Atmospheric Phase And Intensity Turbulence For Long-Path Distance Interferometer," Proc. 3.sup.rd Meeting On Lightwave Sensing Technology, Appl. Phys. Soc. of Japan, 39 (1989). However, the interferometer of Zhu et al. has insufficient resolution for all applications, e.g. sub-micron interferometry for micro-lithography.
A recent attempt at high-precision interferometry for micro-lithography is represented by U.S. Pat. No. 4,948,254 issued to A. Ishida (1990). A similar device is described by Ishida in an article entitled "Two Wavelength Displacement-Measuring Interferometer Using Second-Harmonic Light To Eliminate Air-Turbulence-Induced Errors," Jpn. J. Appl. Phys. 28(3), L473-475 (1989). In the article, a displacement-measuring interferometer is disclosed which eliminates errors caused by fluctuations in the refractive index by means of two-wavelength dispersion detection. An Ar.sup.+ laser source provides both wavelengths simultaneously by means of a frequency-doubling crystal known in the art as BBO. The use of a BBO doubling crystal results in two wavelengths that are fundamentally phase locked, thus greatly improving the stability and accuracy of the refractive index measurement. However, the phase detection means, which employ simple homodyne quadrature detection, are insufficient for high resolution phase measurement. Further, the phase detection and signal processing means are not suitable for dynamic measurements, in which the motion of the object results in rapid variations in phase that are difficult to detect accurately.
In U.S. Pat. No. 5,404,222 entitled "Interferometric Measuring System With Air Turbulence Compensation," issued to S. A. Lis (1995), there is disclosed a two-wavelength interferometer employing the dispersion technique for detecting and compensating refractive index fluctuations. A similar device is described by Lis in an article entitled "An Air Turbulence Compensated Interferometer For IC Manufacturing," SPIE 2440 (1995). Improvement on U.S. Pat. No. 5,404,222 by S. A. Lis is disclosed in U.S. Pat. No. 5,537,209, issued July 1996. The principal innovation of this system with respect to that taught by Ishida in Jpn. J. Appl. Phys. (cited above) is the addition of a second BBO doubling crystal to improve the precision of the phase detection means. The additional BBO crystal makes it possible to optically interfere two beams having wavelengths that are exactly a factor of two different. The resultant interference has a phase that is directly dependent on the refractive index but is substantially independent of stage motion. However, the system taught by Lis has the disadvantage that it is complicated and requires an additional BBO crystal for every measurement path. In that micro-lithography stages frequently involve six or more measurement paths, and that BBO can be relatively expensive, the additional crystals are a significant cost burden. An additional disadvantage of Lis' system is that it employs a low-speed (32-Hz) phase detection system based on the physical displacement of a PZT transducer.
It is clear from the foregoing, that the prior art does not provide a practical, high-speed, high-precision method and corresponding means for measuring refractive index of air and measuring and compensating for the optical path length effects of the air in a measuring path, particularly the effects due to fluctuations in the refractive index of the air. The limitations in the prior art arise principally from the following, unresolved technical difficulties: (1) Prior-art heterodyne and superheterodyne interferometers are limited in accuracy by fluctuations in the refractive index of air; (2) Prior-art dispersion techniques for measuring index fluctuations require extremely high accuracy in interference phase measurement, typically exceeding by an order of magnitude the typical accuracy of high-precision distance-measuring interferometers; (3) Obvious modifications to prior-art interferometers to improve phase-measuring accuracy would increase the measurement time to an extent incompatible with the rapidity of stage motion in modern micro-lithography equipment; (4) Prior-art dispersion techniques require at least two extremely stable laser sources, or a single source emitting multiple, phase-locked wavelengths; (5) Prior-art dispersion techniques in micro-lithography applications are sensitive to stage motion during the measurement, resulting in systematic errors; and (6) Prior-art dispersion techniques that employ doubling crystals (e.g. U.S. Pat. No. 5,404,222 to Lis) as part of the detection system are expensive and complicated.
These deficiencies in the prior art have led to the absence of any practical interferometric system for performing displacement measurement for micro-lithography in the presence of a gas in a measurement path where there are typically refractive index fluctuations and the measurement path is comprised of a changing physical length.
Accordingly, it is an object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the refractive index may be fluctuating and/or the physical length of the measurement path may be changing.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the accuracy of measurements and monitoring of the refractive index of the gas and/or of the optical path length effects of the gas are substantially not compromised by a rapid change in physical length of measurement path.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the method and apparatus does not require measurement and monitoring of environmental conditions such as temperature and pressure.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the method and apparatus may use but does not require the use of two or more optical beams of differing wavelengths which are phase locked.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the optical path length effects of a gas in a measurement path wherein the lengths of measuring paths in an interferometric measurement are substantially not used in a computation of the optical path length effects of the gas.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the frequencies of the optical beams used in an interferometric measurement and monitoring of the refractive index of a gas in a measurement path and/or the optical path length effects of the gas are substantially not used in a computation of the relative contribution of the optical path length effects of the gas.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter. The invention accordingly comprises methods and apparatus possessing the construction, steps, combination of elements, and arrangement of parts exemplified in the detailed description to follow when read in connection with the drawings.